Mathematical Physics


The Divergence Myth in Gauss-Bonnet Gravity

Authors: William O. Straub

n Riemannian geometry there is a unique combination of the Riemann-Christoffel curvature tensor, Ricci tensor and Ricci scalar that defines a fourth-order Lagrangian for conformal gravity theory. This Lagrangian can be greatly simplified by eliminating the curvature tensor term, leaving a unique combination of just the Ricci tensor and scalar. The resulting formalism and the associated equations of motion provide a tantalizing alternative to Einstein-Hilbert gravity that may have application to the problems of dark matter and dark energy without the imposition of the cosmological constant or extraneous scalar, vector and spinor terms typically employed in attempts to generalize the Einstein-Hilbert formalism. Gauss-Bonnet gravity specifies that the full Lagrangian hides an ordinary divergence (or surface term) that can be used to eliminate the curvature tensor term. In this paper we show that the overall formalism, outside of surface terms necessary for integration by parts, does not involve any such divergence. Instead, it is the Bianchi identities that are hidden in the formalism, and it is this fact that allows for the simplification of the conformal Lagrangian.

Comments: 5 Pages. Inserted a missing factor of 2 on the RHS of Equation (3.7)

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Submission history

[v1] 2016-11-13 20:51:33
[v2] 2016-11-15 18:11:29
[v3] 2017-10-03 18:23:05

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